1. skip
2. Ocean and Natasha are two friends who live in Delhi and New York
respectively. Ocean and Natasha only care about consuming bread
and wine, and have identical preferences. Ocean spends his entire
income on 9 glasses of wine and 4 loaves of bread, paying 300
rupees per glass and 500 rupees per loaf in Delhi. Natasha has an
income of $15 and faces prices of $2 per glass of wine and $0.5 (i.e.
50 cents) per loaf of bread in New York.
a. Draw their budget constraints on the same graph.
b. Can we conclude from the information above that Natasha
must be worse off than Ocean, (and would therefore prefer
his budget set than her own) ?
3. A consumer with strictly convex preferences consumes two goods
𝑥! and 𝑥" . Suppose 𝑥! is a Normal Good and an Ordinary Good. Show
using indifference curves the Slutsky income and substitution
effects of a price increase for 𝑥! from 𝑝! to 𝑝!# . Denote the price of
good 2 by 𝑝" , and income by 𝑚.
Note: make sure to draw a large graph, where intersections vs. tangencies, and
parallel vs. not parallel lines can be identified. Indifference curves should not
intersect. Label slopes and intercepts.
4. A firm that uses inputs 𝑥! and 𝑥" , has a production function that is
given by 𝑓(𝑥! , 𝑥" ) = +min {𝑥! , 𝑥" }
a. What kind of returns to scale does this firm experience?
Explain.
b. If the two inputs 𝑥! and 𝑥" cost $3 and $4 per unit
respectively, what is the total cost function 𝑐(𝑦) of this firm?
Hint: do not use the Lagrangean to solve this problem as the
production function is not differentiable. Ask yourself, if the
firm had to produce, say, 8 units, what input combination will
do so in the cheapest way? What would the answer be if it
wanted to produce 𝑦 units?
c. If the firm is in a perfectly competitive market and the current
market price for its output is $100 per unit, how many units
will the firm supply at this price? Explain.
5. There is a single motel (a monopolist) in the town of Elyria, OH.
Demand for rooms is given by 𝑞 = 200 − 2𝑝. The marginal cost of a
room is $10/night.
a. What will be the price of a room in this market?
b. What is the price elasticity of demand at the equilibrium output
level?
c. What is the deadweight loss of this monopoly? Show your work.
6. A monopolist sells bottles of mineral water to two customers: the
high demand customer’s demand is described by
𝑞$ = 50 − 𝑝$
and the low demand customer’s demand is described by
𝑞% = 30 − 𝑝%
The total willingness to pay of a consumer for 𝑞 units is the area
under their inverse demand curve till 𝑞 units. The costs of
production are 0. Suppose the monopolist cannot distinguish
between the two consumers and is thinking about offering each of
the customers two options:
Option A: buy 50 bottles for a total payment of $𝑦
Option B: buy 25 bottles for a total payment of $𝑥.
Consumers buy the option that gives them a higher net consumer
surplus. They can only buy a single option, and a single unit of it.
a. Suppose 𝑥 is set equal to the total willingness to pay of the
low demand customer for 25 bottles. Compute 𝑥.
b. Given your answer for 𝑥, what 𝑦 should the monopolist set
to maximize profits? Explain.
7. Jia and Megha are two Christmas tree sellers on W 95th St, where
the demand curve for trees is described by 𝑝 = 500 − 𝑄, where 𝑄 =
𝑞& + 𝑞' , and 𝑞( is the output of seller 𝑖 = 𝐽, 𝑀. Each seller’s total cost
function for producing trees is 𝑐(𝑞( ) = 10 + 𝑞(" .
a. Suppose Jia believes that Megha will bring 𝑞B' trees to the
market. How many trees should Jia bring to the market in
response to this belief? Explain.
b. What is the Cournot-Nash equilibrium level of outputs (such
that neither seller wants to change their output, given the
output of the other seller). Explain.
c. If this was a perfectly competitive industry, with a large
number of sellers like Jia and Megha, what would be the longrun equilibrium price and quantity sold per seller? Assume
that 𝑐(𝑞( ) above is the long run cost function of the firms, for
𝑞( > 0, and for 𝑞( = 0, 𝑐(0) = 0. [Note: you can do this part
even if you were unable to do the first two.]
8. There are two consumers, A and B, in an economy, who consume
two goods, 𝑥 and 𝑦. A is endowed with 3 units of 𝑥 and 2 units of 𝑦.
B’s endowment is 4 units of 𝑥 and 5 units of 𝑦. A and B’s utility
functions are 𝑈) (𝑥, 𝑦) = 2𝑥 + 𝑦 and 𝑈* (𝑥, 𝑦) = 𝑥 + 𝑦.
a. Define a Pareto Optimal allocation. Is the initial endowment
allocation Pareto Optimal? Explain.
b. Draw an Edgeworth box for this economy, and show the initial
endowment, and the indifference curves passing through the
initial endowment (label their slopes and intercepts).
c. Show on the graph the allocations that are Pareto-superior to
the endowment, if any. Show the contract curve (the set of all
the Pareto Optimal allocations) in this economy. Explain.
9. An airport is located next to a housing developer’s project. Let 𝑥 be
the number of noisy planes that fly at the airport every day and let 𝑦
be the number of houses the developer builds. The airport’s total
profits are
𝜋) (𝑥) = 32𝑥 − 2𝑥 "
and the developer’s total profits are
𝜋+ (𝑥, 𝑦) = 70𝑦 − 4𝑦 " − 𝑥𝑦.
The airport says to the developer: “you decide how many flights I
should fly but then you must compensate me for any loss in my
profits as a result.”
a. How many flights will the developer ask the airport to fly?
b. How much compensation, if any, will the developer pay the
airport?
Show your work.